Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

Question

p2 − 18p +

Answer 1

To complete the square for the polynomial \( p^2 - 18p \), we will follow these steps:

1. Take the coefficient of the linear term, which is \(-18\).
2. Divide it by 2: \[ -18 \div 2 = -9 \]
3. Square this result: \[ (-9)^2 = 81 \]

Therefore, the number that makes the polynomial a perfect-square quadratic is 81.

Thus, the completed square form of the polynomial will be: \[ p^2 - 18p + 81 = (p - 9)^2 \]